Manuel Pellegrini acclaimed this victory as Manchester City's best performance of the season but it was another headbutt incident on a tempestuous afternoon that demanded most attention. The City goalkeeper, Joe Hart, was at the centre of it, shoving his head towards the face of Hull's George Boyd after his opponent went down under his challenge in the penalty area. All this just a fortnight after Alan Pardew was heavily reprimanded for an altercation with David Meyler at the same ground.

Both teams played down the heated exchange in the 69th-minute, the video evidence also hinted at Boyd spitting – proving intent would be difficult. Pellegrini insisted he could not see the fracas clearly from his touchline position while the Hull manager, Steve Bruce, dismissed comparisons to Pardew and praised Lee Mason's handling of things. "He was on the spot and made the right decision," said Bruce. "We've all seen handbags before and as far as I could see he deserved the yellow card, and that was enough punishment. Certainly I didn't see him [Hart] put a head in there, I saw them go head to head but not any action like that."

Hart, incensed by Boyd hitting the turf after minimal contact with his trailing leg, squared up to his opponent and the pair were separated by team-mates. The blood was still up on both sides when, with the visitors still 1-0 ahead, Fernandinho's muscular challenge on Boyd in the area went unpunished by Mason.

Earlier, the official dismissed Vincent Kompany, the City captain, for denying Nikica Jelavic a goal-scoring opportunity in a week that included elimination from the Champions League and FA Cup appeared to be taking another turn for the worse. However, City's tendency to make it difficult for themselves– this was their third red card in the past fortnight – did not prove critical as David Silva scored an exquisite opener and crafted the late second for Edin Dzeko.

Asked if this was the best display his team had given this season, Pellegrini said: "I think so. It was a very good response in a very difficult week. We lost against Wigan and Barcelona and we needed to win. Playing with one player less for 80 minutes is very difficult, but I trust in the team and we did very well with the ball and without it."

The lunchtime kick-off provided an opportunity to transfer some of the pressure in the title race back on Chelsea, who began nine points clear but having played three matches more. But their prospects nosedived when Kompany, grappling for possession with Jelavic deep into the visitors' territory, lost his footing and had crucially conceded a yard by the time he regained it.

Fuming that Mason had failed to penalise Jelavic for what he saw as the original infringement, the Belgian kicked the wall on his way down the tunnel.

The portents for an away win were not good: City's previous victory in a league encounter in Hull came on their first visit back in 1909. But having not been given a moment's peace by Hull when it was 11 versus 11, City took the lead four minutes into their numerical disadvantage as Silva exchanged passes with Yaya Touré and clipped a delicious left-foot effort in off the post from 25 yards.

Content to sit back and hit the home team on the break, City were close to doubling their advantage with their only other notable effort of the opening period, when Pablo Zabaleta accepted a deflection into his path and watched as his dipping volley crashed down off the crossbar. Television technology revealed some – but crucially not all – of the ball had crossed the line.

Despite their best endeavours – abetted by Bruce's offensive alterations –Hull could not find their way back into the match. This was the 15th time they had gone behind this season, and their 14th defeat in such circumstances.

Fernandinho and Dzeko squandered opportunities to settle things in the final quarter of the match when through one on one with Allan McGregor. However, Dzeko made no mistake when sent beyond the home backline by a delicate flick of Silva's boot in the final minute.

"Will we ever have a better opportunity to beat them? In the end it became one of those frustrating afternoons," said Bruce.

"Our game plan was out of the window after 10 minutes. We thought we would be playing Manchester City on the counter-attack rather than having the lion's share of possession and them camped in their own half, and we didn't have the quality to break them down."